A GAME-THEORETIC ANALYSIS OF THE WATERLOO CAMPAIGN AND
SOME COMMENTS ON THE ANALYTIC NARRATIVE PROJECT*
by Philippe MONGIN, CNRS & HEC School of Management**
Cahier du GREGHEC/ GREGHEC Working Paper no 915 Ecole HEC /HEC School of Management
April 2009
Abstract : The paper has a twofold aim. On the one hand, it provides what appears to be the first game-theoretic modeling of Napoleon’s last campaign, which ended dramatically on 18 June 1815 at Waterloo. It is specifically concerned with the decision Napoleon made on 17 June 1815 to detach part of his army against the Prussians he had defeated, though not destroyed, on 16 June at Ligny. Military historians agree that this decision was crucial but disagree about whether it was rational. Hypothesizing a zero-sum game between Napoleon and Blücher, and computing its solution, we show that it could have been a cautious strategy on the former's part to divide his army, a conclusion which runs counter to the charges of misjudgement commonly heard since Clausewitz. On the other hand, the paper addresses methodological issues. We defend its case study against the objections of irrelevance that have been raised elsewhere against “analytic narratives”, and conclude that military campaigns provide an opportunity for successful application of the formal theories of rational choice. Generalizing the argument, we finally investigate the conflict between narrative accounts – the historians' standard mode of expression – and mathematical modeling.
Keywords: Napoléon, Blücher, Grouchy, Waterloo, military history, rational choice theories, game theory, zero-sum two-person games, analytical narrative
JEL Classification Numbers: N43, C72, B49
* An earlier French version was circulated in 2007-08. The author thanks Eli Spiegelman for preparing the translation from which the current English version evolved. He also acknowledges helpful comments from Alain Boyer, Bruno Colson, Mikaël Cozic, Françoise Forges, Brian Hill, Antoine Lilti, Bermard Manin, André Orléan, Bernard Walliser, and the participants of seminars or conferences at Université de Genève, Université de Strasbourg, Université de la Réunion, and the London School of Economics, where he presented the paper.
1. Introduction
Once launched in economics and its attendant disciplines, theories of rational choice spread abundantly beyond this original realm. An entire branch of experimental psychology is now devoted to them. Schools of sociology and political science align themselves with the theories, against others which reject them. Indeed, the resistance offered by these latter two disciplines has sparked well-known controversies, some of which have gone on to become academic topoi (think for instance of that which has wracked the sociology of education for years). But history has escaped this trend, even, so it would seem, in its critical form. Not only has the discipline been reluctant to make use of rational choice theories, but it has also shown itself little inclined to reflective debate on their possible applications. Those who reject cost-benefit analyses are not likely to conduct one to see whether or not it is useful to do so.
A few authors – actually more political scientists or economists than historians – would now break this status quo by promoting “analytic narratives”. The term, which has become something of a rallying cry, sounds more abstract than the movement’s true objective, which is primarily to apply game theory to traditional topics of political history: municipal conflicts in medieval Genoa, the tax systems of prerevolutionary Europe, conscription laws in the 19th Century, entry of new states to the American federation, regulation of the coffee exchange at the end of the 20th Century. Such an exception is too curious to pass unnoticed. But it has hardly generated a craze. The methodology has been criticized on the grounds that, first, the historical cases have been ill-chosen, second that the models used to explain them do not adhere to the strictest norms of rational explanation, and third that these very norms themselves are dubious.1 The present paper also employs game theory to inform the study of history. It is another attempt to implement the “analytic narrative” methodology, but with a shift that its choice
1 The studies are due, respectively, to Greif, Rosenthal, Levi, Weingast and Bates. They have been brought
together in Analytic Narratives (1998), which is a manifesto for the group. The three levels of criticisms are found in Elster, to whom the authors have replied; see this important controversy in the American Political Science Review (2000, p. 685-702).
of a military topic will make clear. By and large, we would endorse the previous writers against objections of the second and third levels, arguing, as they forcefully did, that there is no obligation to be theoretically sophisticated in applied work, and that it is not very helpful in the present context to rehearse the classic problems of rational choice theories.2 But objections of the first level are different, and here we certainly agree with the critics that few historical topics are amenable to “analytic narratives”. We propose the rule that the selection of cases be justified explicitly in terms of the questions the earlier historians have raised and the data they have left to answer them. Game theory should be connected with preexisting accounts of the usual style more tightly than has been done so far. As a companion rule, we propose that the author of an “analytic narrative” state also explicitly what he aims at eliciting from the historical material that cannot be obtained by ordinary narratives, and why this material calls for his specific modeling rather than any other. Again, the previous work appears to be somewhat elusive in this respect.
With these guidelines in mind, we tried the “analytic narrative” methodology on Napoleon’s last campaign in June 1815 - that which he eventually lost to Wellington and Blücher on the battlefield of Waterloo. One broad reason for this choice is that military studies have often served as a touchstone to rational choice explanation. That they are a fertile terrain for such activity has been suggested a number of times. For example, Pareto (1917-1919, §152) classes them among the few disciplines - along with economics and technology - that embody his concept of “logical action”. Among military studies overall, the account of battles and campaigns appears to be more tractable than others. Thus, to illustrate his ideal-type of “instrumental rationality”, Weber (1922a, p. 10; Eng. ed. p. 21) mentions the Prussian Moltke and the Austrian Benedek fighting each other at the Sadowa battle. Even more clearly, the authors of campaign narratives, beginning with Jomini and Clausewitz in the 19th Century, have given flesh to the view that their field has a special susceptibility to rational choice explanation.
2 Unless this serves to argue that rational choice theories are absolutely flawed or irrelevant. See the final
comment by Bates and al. in their reply to Elster: “His real opponent is rational choice theory” (2000, p. 702).
This recognized exemplary character of military studies, and above all, campaign narratives should be of interest to the “analytic narrative” writers and their fellow-travelers. From this point of departure, they could hope to pass more easily through the strictures set by the first level of objections, and thus to establish a genuine dialog with professional historians, who seem a little more disposed here than elsewhere to relax their longstanding mistrust of rational choice theories. In this group, game theory enjoys a place of natural support since its technical concepts – beginning with that of the strategy – have intuitive relationships with the military use. Admittedly, von Neumann and Morgenstern (1944) did not pay much attention to military affairs, giving greater importance to parlor games in their examples. But their followers at the RAND Corporation and in US military institutions dealt with nuclear strategy and deterrence at considerable length, and even more relevant to our project, one author in this group, Haywood (1950, 1954), undertook a game-theoretic analysis of some battles of the Pacific War, using the basic tool of von Neumann and Morgenstern, i.e., zero-sum two-person games.3
Military applications pay for their didactic facility with a clear disadvantage. Though they may succeed in their ambitions, they have not the same demonstrative consequences as if they had taken on more resistant subjects such as medieval Genoa or the finances of prerevolutionary France. So be it with the present work. Its aim is really to restart the debate on “analytic narratives” from a middle ground that can be accepted by the less passionate critics. We would be entirely satisfied if we made consensual a bare existential point: there is a class of plausible historical applications for game theory. The controversy has been so fierce that even such a weak claim was not taken for granted among the participants.
What can be claimed for game theory can also be for the theory of individual decision-making under risk and uncertainty, or decision theory in the narrow technical sense. For the latter is usually construed as a special case of the former, and it is anyhow a logical prerequisite for it. Despite these clear connections, military applications with just one
agent facing nature are worth exhibiting; we provide one elsewhere by borrowing again from the Waterloo campaign.4 In contrast, it is an open and very intriguing question whether some use in history may ever be found for the aggregative theories of social choice. At any rate, we stop at the classic trio of microeconomics texts. What we are not
addressing are the “rational choice theories” in the informal sense often favored by social sciences other than economics. The case for rational choice explanation in history has already been made vis-à-vis such informal conceptions with rather plausible examples and arguments, and there would be no point in restating it.5 By the same token, the only models of interest will be those applying one of the theories above to particular histories – hence they will be mathematical, not informal models. In thus constricting our subject matter, we highlight the most spectacular conflict of all, i.e., that between a liberal (in several senses) discipline and a set of tools so coarse and uncouth as to be perhaps beyond assimilation. Seemingly an oxymoron, the slogan of the “analytic narrative” underlines this tension well.
Among the topics available in military history, ours is scarcely original, but this is perhaps more of an asset rather than a liability, given the previous guidelines. An old chestnut from the strategy courses of staff colleges in the 19th Century and early 20th Century, Napoleon’s 1815 campaign has remained an inexhaustible and fascinating subject for war historians up to the 21st century. The rich bibliography in three major languages is an attraction of the case. An even more important reason for selecting it is that, despite so much available evidence, historians have been unable to come to agreement on how to explain Napoleon’s stupendous disaster, and what they disagree precisely on is the rationality of this prominent actor. The game-theoretic modeling may renew the time-honored controversies, and if it does, the resulting “analytic narrative” may be welcome by even some of the critics.
4 Mongin (2009) suggests reconstructing several passages in Clausewitz’s account of the campaign in terms
of individual expected utility maximization. The full game-theoretic perspective is unnecessary to account for the agents’ decisions in these passages.
The controversies go back to an account the overthrown emperor dictated at Sainte-Hélène to his companions in exile, which was a plea pro domo. Among the texts recording it, we have selected Mémorial de Sainte-Hélène by Las Cases because it is the most widely distributed and the most succinct.6 Napoleon's line is to lay the blame for defeat with marshals Grouchy and Ney, who he claims misjudged their strategic possibilities and did not properly follow his instructions. However, Clausewitz, who had access to Memorial as well as further French and German sources, reached the opposite conclusion that the underlings might be pardoned and the hero should not be exculpated. The first genuine scholar of the campaign, the Prussian general is also a passionate critic of Napoleon’s handling of it. With various nuances, his position has carried the day in the literature, but the imperial argument, long upheld by French military writers, has not disappeared altogether. One meets it still today, with qualifications that leave it no less worth considering than the other. So historians are in a deadlock, and after so much time, there seems to be little hope that progress will be made by traditional means; this is our best justification for trying the “analytical narrative” perspective.
Clausewitz’s interpretation is to be found in a monograph, The Campaign of 1815 in France, which the treatise On War has regrettably overshadowed, and it is a secondary aim of this paper to draw attention to that part of his work.7 In it, one can find anticipated
use, if not yet the full realization, of Weber’s principle of instrumental rationality (henceforth, we simply say “the principle of rationality”). By contrast, the concepts of ends and means that direct the classic definitions of war in the treatise spring from an abstract teleology, detached from acting individuals, which is not the same as that clarified in Weber's methodology. Another contribution of the monograph is that, while following the principle of rationality throughout, it now and then surpasses the level of
6 Las Cases includes “Relation de la campagne de Waterloo, dictée par Napoléon” in Mémorial de Sainte-Hélène under the date of 26 August 1816. The other references are Gourgaud’s La campagne de 1815 and Bertrand’s Cahiers de Sainte-Hélène. The last work was published long after its author’s death and played no role in the Waterloo controversy, contrary to the first two, which came out in 1823 and 1818 respectively.
7 Der Feldzug von 1815 in Frankreich. Posthumous like the others, this work appeared in 1835 in the Hinterlassene Werke edited by Marie von Clausewitz; it was written in 1827. Clausewitz’s commentators have not spent much time on his campaign narratives. For instance, Aron (1976) hardly mentions them at all and Paret (1992, ch.9) is somewhat quick and derogatory with them.
generality at which historians normally stop, suggesting – even sketching out – models in the sense relevant here. These anticipations are all the more intriguing since, contrary to
On War, The Campaign is a historical work; it alternates between traditional narrative and logical argument that opens the way to contemporary formalization. We will actually rebut Clausewitz’s substantial interpretation of Waterloo, but praise his general method, and the “analytic narrative” school may be pleased to register him as a glorious precursor. Section 2 of this paper reviews the main facts and interpretations of the campaign, emphasizing those which matter for the model to come. It will go light on the tactical aspects of the battles, even the major ones of Ligny and Waterloo, and focus on the overall strategy as Napoleon might have conceived of it. This passage intentionally reproduces the standard narrative mode of military historians.
Section 3 changes tone, proposing a model for Napoleon’s all-crucial decision, June 17, 1815, the day after his victory over Blücher at Ligny. That day he chose to send more than a third of his forces, under the command of Grouchy, against the retreating Prussians. All the commentators agree that this division of the French army was the key to Wellington’s victory, June 18 at Waterloo. Grouchy spent the fateful day at Wavre, baited by Blücher’s rear guard, while the advance guard marched unimpeded to join Wellington in the mist of an uncertain battle. The campaign’s greatest question, which involves Napoleon’s rationality, is whether he could have made better use of Grouchy’s detachment. The model we propose to answer this question takes the form of a simple zero-sum game between Napoleon and Blücher. Despite the absence of Grouchy as an autonomous player, it adds precision to the competing hypotheses. In the end, we will side with the proNapoleonic minority against the Clausewitzian majority. Rational choice modeling, which supplies the arguments, will have thus played its customary charitable role vis-à-vis the agent.8
9 Davidson (1980) is famous for emphasizing the principle of charity underlying that of rationality. His
argument is that we cannot understand others except rationally, and this requires that we also understand them charitably.
Section 4 subjects the model to the same three levels of criticism brought against the “analytic narrative” methodology, and pursues the argument sketched above for applying it to existing campaign narratives. Section 5 explores the methodological tension that even such cautiously restricted studies cannot avoid. To eventually reconcile the new narrative style with the old one, we will defend the idea that they support each other by the complementarity of their faults. A standard historical narrative performs several useful functions at once, but as we argue, does not take any of them to their final stage; in particular, say what the historians might, its explanatory role remains very imperfect. The missing steps can be achieved by models from rational choice theories, which will have the opposite weakness of serving too few purposes at a time. Thus, the strategic game constructed for June 17 goes somewhat farther in explaining the events of that day than the available accounts, but it has the drawback of sacrificing the expressive and evaluative functions that these accounts also supply, and hence should not aim at replacing them. Clausewitz's alternation between standard narrative and (in his case only suggested) technical modeling is the only feasible scheme for an analytical history.
2. The Waterloo Campaign: main facts and interpretations.
In the spring of 1815, a coalition of the European powers was solidifying against France. Napoleon needed to annihilate the two armies already mounted – the English and the Prussian – as quickly as possible. Against Wellington’s 93,000 Anglo-Dutch soldiers, who were preparing to meet Blücher’s 118,000 Prussians in Belgium before invading France, Napoleon had only the 124,000 troops of Armée du nord; his other forces covered the Rhin or garrisoned fortresses. The only way out was to reproduce his masterstroke from the Italian campaign: first defeat one army, then the other. All historians recognize this plan, and most of them, including Clausewitz, hold that it was the only one conceivable.9 At first, the execution seemed promising. With his customary swiftness, Napoleon entered Charleroi on June 15, forcing the Prussian advance guard to pull back northeast of the city. The allies had not yet joined forces, and each group alone
9 La campagne de France en 1815, tr. by Niessel, 1973, p. 37-43. From now on, all page references to
left much to be desired. The Anglo-Dutch were deployed widely around Brussels and westward, as Wellington wanted at all costs to maintain communications with Ostend in that direction.10 And Blücher was headquartered in Sombreffe, some 12 kilometers northeast of Charleroi, with only three corps; a fourth, commanded by Bülow, kept the rear guard and was useless for battle. In taking this forward position Blücher ran the risk of confronting Napoleon with insufficient forces. However, his decision becomes clearer in the light of the agreement he had reached with Wellington on May 3, to the effect that the allies would meet on the Quatre-Bras-Sombreffe line in the case of an offensive by Napoleon. This strategy ran afoul of the classical precept of maximal preliminary grouping, but Blücher could hope that Wellington would play his agreed-on part in the fight.
The Prussians had occupied the hamlet of Ligny, which gave its name to the battle that they ended up pitching alone there, over the afternoon and the beginning of the evening of June 16. Less famous than that of June 18, this battle actually determined the succeeding chain of events, and it is with regards to its interpretation that the main hypotheses square off. The Campaign, to quote but one account, gives more space and emphasis to Ligny than it does to Waterloo.
Blücher’s risky strategy, which Napoleon immediately recognized, offered him an opportunity to carry out his campaign plan. He won on June 16 following the two standard criteria of victory: lose fewer men than the adversary, and conquer the terrain of the battlefield. While very real, this victory was not yet decisive. Blücher managed to save most of his forces, some 90,000 men, in sufficient order to bring them back to his rear guard. So his initial error – leaving Bülow in reserve – would eventually turn to his and Wellington's advantage. In the Memorial, Napoleon implies that the three Prussian corps engaged at Ligny escaped destruction through Ney's fault.11 In fact, he had sent the marshal away in the north-west direction with the principal objective of holding the road
10 Hofschröer (1998-1999) stresses that Wellington had weakened himself to prepare for an attack from the
west, which there was little reason to expect. The Duke had already faced the charge in his reaction to Clausewitz; see Bassford (1994, p. 42-45, and 2001 for a transcript of Wellington’s comments).
from Charleroi to Brussels, which Wellington would have to use if he came in support of Blücher. Ney’s group - about 25,000 men under his direct command - had the option of either attacking the Anglo-Dutch, or simply holding them back, while taking the Prussians from behind. Napoleon mentions both tasks at once, which is much to ask of poor Ney, considering both his resources and his actual capacity for initiative. At the field of Quatre-Bras, where he met the English forward guard, he carried out the former task slowly and awkwardly, not even considering the latter. The corps of Drouet d’Erlon – 20,000 more men - was to come to Ligny or Quatre-Bras in case of need, but wandered piteously from field to field without engaging; many have seen in this a turning point in the campaign.
Clausewitz defends Ney by arguing that the successive orders that Soult, the campaign’s chief of staff, sent him in the name of the Emperor were incompatible. This analysis, which we will not develop here12, brings out the rationality principle most clearly: “Ney absolutely completed his goals – to block the aid of Wellington. Bonaparte did not come to the idea of having him cooperate in the battle of Ligny until later, after having recognized Blücher’s position…. Only today can we see [what Ney could have done], by bringing into our calculations all the fortuitous circumstances that could not be foreseen at the time” (Clausewitz, p. 105). Weber would not distinguish any better than that between objective rationality, which can be identified from the perspective of an observer looking back, and the subjective rationality of individuals, which is the only pertinent type for explaining their actions.13
Starting a movement that would turn out to be decisive, the Prussians did not back up along their natural line of communication, which was the Meuse river valley, but farther northward, in the general direction of Louvain. They regrouped over the course of June 17 at Wavre, a town situated on the river Dyle, mid-way between Ligny and Louvain. This location allowed them to keep as many options open as possible. From there, Blücher could either organize a definitive retreat by reaching Liège by way of Louvain,
12 More on it in Mongin (2009).
13 Cf. Weber (1922b, p. 435-439). The distinction between objective and subjective rationality has since
or rejoin Wellington, who was a single day’s march away. On the same day, Napoleon chose to separate his right wing, which Grouchy had commanded at Ligny, of some 30,000 men. With this detachment, the marshal could either set loose a savage chase against the Prussian rear, without worry of what became of the rest of that army, or keep this army once joined from meeting the Anglo-Dutch, or to carry out the objectives of pursuit and blocking to the extent that they were compatible.
What actually occurred is that Grouchy set off after the Prussians, who intentionally slowed one of their corps, led by Thielemann. On June 18, the marshal pitched battle at Wavre against just this rear guard. Meanwhile, the advance guard, with Bülow and Pirch, marched unobstructed to Waterloo, and it bowled into the French right on the afternoon, early enough to help Wellington, who was not in an easy position.14 Having missed the
chance the first time because of Wellington, the allies succeeded in concentrating their forces the second time thanks to Blücher. It is unlikely that Grouchy would have brought the French victory in a battle including Bülow and Pirch, but if he had been there instead of the two Prussians, he would have given Napoleon the numerical advantage needed to defeat Wellington. The two commanders faced 70,000 men each against one another, and equality favored the latter, who had chosen to fight from a strong defensive position, as he had done to his advantage so often before.
As already indicated, a major problem of the campaign is to decide what Napoleon intended to achieve with Grouchy’s detachment. It is closely connected with another, which is to decide how Napoleon interpreted the battle of Ligny. To what extent did he overestimate the extent of his victory, and misjudge the direction of their retreat? Clausewitz (p. 107-109 and 146-148) claims that he made mistakes on both counts, and this has dominated the literature since. Let us review the evidence available to answer the two questions.
14 Although Thielemann had finally to surrender Wavre, he had fulfilled his role by holding the enemy for
Napoleon's initial orders to Grouchy on June 17 were oral, and neither the Memorial nor the marshal’s Memoirs are reliable enough to permit reconstructing them.15 Clausewitz, in his chapter XXXVII, claims that Napoleon entrusted Grouchy with a simple mission of pursuit. This, together with an error that Napoleon made concerning the direction of the Prussian retreat, would cleanse the marshal of all responsibility in the next day’s rout - busy in the east, Grouchy could not at the same time lend a hand to Napoleon. The conclusion is implacable if one accepts the premises, but Clausewitz has little more than hints to establish these, and his supporters to this day have not substantially improved the argument.16 As it had done with Ney, the Memorial (p. 245) charges Grouchy with responsibility for the defeat, claiming that he should have been on the Waterloo battleground. French military writers have often taken this position, while softening it with additional reproaches against Napoleon, and still more against his chief of staff Soult.17 A good deal of this is transparent apology; however, there are also historians
without any emotional stake, such as the 20th Century British general Fuller (1951-1956, ch. 18), who concludes that Grouchy ended up in a place he should not have been.18 None in the present group of commentators could accept Clausewitz’ narrow interpretation of the orders of June 17. Napoleon by their reading, unsure of whether the Prussians had been truly beaten, would have asked Grouchy to protect him from their intrusion into the following battle. He would thus have entrusted Grouchy with a role of blocking or interposing at the same time as one of pursuit. This wider interpretation obviates the problem of what Napoleon precisely thought of the direction of the Prussian retreat. There were two possibilities: either the entire Prussian force had moved east, in which case the chase would also serve as interposition; or else the enemy was dispersed, with some forces taking the dangerous way to the west, in which case Grouchy should prioritize the objective of blocking over that of pursuit. This line has no more solid proof than the other; what is known of the 17 June does not permit a clear winner in the historical contest.
15 Compiled by his descendants, Grouchy’s Mémoires discuss these instructions at length, but the effort at
exculpation is so blatant that it is impossible to take them seriously.
16 Even the careful study by Hofschröer (1998-1999) is far from making Clausewitz’s case compelling. 17 Mauduit (1847) eloquently illustrates the beginning of this line of interpretation, the first of many to
incriminate the weakness of Soult and the staff in general.
The first written communication that follows the oral commands of June 17 is a letter dictated to Bertrand, received by Grouchy shortly after he set off. Both interpretations can find something in it, the first because it sends the marshal towards Gembloux, i.e., to the east, and even worse, towards Namur, which distanced him from the Prussians, and the second because it directs him to report on Blücher’s maneuvers, and even to warn the staff of any possible intention to join Wellington.19 From Gembloux, where he did not arrive before the late evening, Grouchy replied to Napoleon with a revealing dispatch. This shows that he had at last understood that Wavre was one of the Prussian destinations, but not yet that it was the only one. Also, Grouchy brings up the possibility of an enemy move towards Wellington, and adds that he would try to prevent it from occurring, which lends some support to the view that the conversation of June 17 had suggested interposition as a goal.20 Although the marshal’s letter arrived at 2:00 in the
morning, the staff’s reply was not sent before 10:00, in which we can see definite evidence of ill-functioning. On behalf of Napoleon, Soult commanded Grouchy to make all haste to Wavre, pushing back any Prussians he finds as he approached the principal army. “His Majesty desires that you direct your movements to Wavre, in order to come closer to us, and to cooperate with our operations”.21 The minority line uses this sentence to argue that Napoleon wanted to have Grouchy participate in the battle of Waterloo (see, e.g., Fuller, 1951-1956, ch. 18). But Clausewitz countered the charge in advance, underlining that it was too late to send orders to Grouchy; in fact, the marshal did not receive them until the afternoon, by which time he had been stuck at Wavre by Thielemann, and Pirch had nearly reached Mont-Saint-Jean.
Regardless of what can be made of the last dispatch, somewhat confused and certainly too late, the strategy was clear in itself. Upon his arrival at Gembloux, Grouchy had to arrange to block the Prussians' move towards Wellington instead of continuing to chase them. Fuller proposes an itinerary consisting of a march to Wavre from the west; thus, the
19 Cited by Mauduit (1847-2006, p. 142) and subsequent authors, Bertrand’s letter is missing from
Clausewitz, which weakens his chapter XXXVII.
20 We use the Mauduit’s (1847-2006, p. 160-161) version of this letter. Fuller (p. 285-286) summarizes it
accordingly, while Grouchy’s Mémoires (LV, p. 58-59) distance themselves significantly from the text.
marshal might intercept the first corps heading to Waterloo. Clausewitz (p. 143) also thinks that the westward march was the best strategy, agreeing for once with the
Memorial (p. 238-240), which first said that very thing.22 It therefore appears that on the limited level of objective rationality, all the interpreters are in agreement. What divides them is how to apportion subjective rationality between the actors on the basis of their beliefs, and this conclusion is impossible to reach simply from the documents we have surveyed.
We will discuss but briefly the final battle. June 17, after the fights of Quatre-Bras, Wellington withdrew his troops to within about ten kilometers of Brussels, on the Mont-Saint-Jean plateau, whose value for defensive combat he had already spotted.23 Partly hidden along the crest, the Anglo-Dutch could pepper their opponents almost at leisure, while the attackers were blocked by solid buildings - farms and convents - in the center and on both flanks. On June 18, rain delayed the French attack until 11:30, and hindered the artillery preparation that Napoleon was accustomed to implement before attacking. For this reason and others, the first offensive, directed against the center of the Anglo-Dutch line, was a complete rout. Several historians, including Fuller, conclude that with such a bad start, Napoleon should have given up fighting the moment he heard of the arrival of the Prussians, that is near 3:30 p.m.24 By moving to the defensive, he might
have saved his army and fled with it back to France. But he did not. He tried to settle the outcome with a sequence of thrusts to the enemy’s center, while simultaneously trying to close the gaps that the Prussians made in his right wing. The specialists have never seen anything but a constant battle plan, but have judged it simplistic, dangerous given the frail right flank, and above all of stunningly feeble tactical execution. Leaving aside the full succession of attacks, we will single out the last and most famous, that is the engagement, around 7:30, of the Old Guard, which was the last available reserve.
22 Houssaye (1905-1961, p. 294-295) explains the desirable path. Grouchy would leave Gembloux by the
west, marching to Mousty and Ottignies, where he would cross the Dyle and follow the river’s left bank.
23 It would be more accurate to call the battle after Mont-Saint-Jean, where it took place, than after the
neighboring village of Waterloo, but Wellington wanted that name to be chosen. The Germans – Clausewitz among them – long preferred to call the battle after the farm of Belle-Alliance, where Blücher and Wellington met in the evening of June 18.
Followed by many others, Clausewitz believes that it was an absolutely hopeless move. He goes as far to claim that Napoleon no longer truly knew what he was doing (p. 158). The moment has arrived for analytically reconsidering the campaign’s main junctures. At three key moments – June 17, around mid-day on June 18, and in the final hours of this same day – Napoleon could have departed from the line of events that his previous decisions had set in motion, and he did not. Is this inertia or lack of reflection, in which case he would no longer conform even to subjective rationality? Or is it a failure to correctly appreciate the situation at hand, in which case this form of rationality could be salvaged? Or is it the case that Napoleon assessed the situation correctly from the perspective of objective rationality, simply accepting the immense risks that this assessment made clear? Essentially, Clausewitz interprets the engagement of the Old Guard as pure and simple irrationality, and the dismembering of the army after Ligny as the result from an incorrect belief held in accordance with subjective rationality. He is more cautious in handling Napoleon’s decision to continue the battle despite the threatening Prussian advance. At this point, he realizes that a taste for risk exacerbated by the circumstances may be consistent with subjective and even objective rationality - the last of the three interpretations we have just sketched out.25
The diagnosis is complicated by Napoleon’s objectives, which were not of the usual military kind. He needed not just to win the campaign, but to win it absolutely; for a weak victory would not have saved France from being invaded and his regime from collapsing. The two goals that Clausewitz usually assigns to war – destruction of the enemy forces and the political advantage that can be taken from the actions, whether victorious or not – were firmly bound together26. The Borodino battle of the Russian campaign, as reinterpreted in On War (IV, 12), will make this clear by way of contrast. There, Napoleon refused to engage his reserves against Kutuzov, consciously giving up a more complete victory that was otherwise within his reach. He was justified in holding
25 See Clausewitz, p. 157. This is a brilliant insight for a time when the concept of risk-attitude was not yet
separated from those of risk or uncertainty; see Mongin (2009).
26 The tension between these two goals of war can be seen throughout On War, and Aron’s (1976, ch. III)
back his limited forces, says Clausewitz, because he meant to enter Moscow in such obvious superiority that the tsar would beg peace from him. Borodino illustrates the long-term political objective separating itself from the short-long-term military objective, a mental situation exactly opposite to that of Waterloo.27 In 1815, the short term was the long term, there was nothing to be gained from restraint, and only by incurring extravagant risks could Napoleon hope to reach his objectives.
Even the brutal sacrifice of the Guard is more ambiguous than it first appears. Recent military analysis permits reconsidering the battle’s last phase. The partial fall of the Anglo-Dutch center around 6:30 afforded Napoleon his best chance of the day. Had he launched the Guard at this moment precisely, rather than an hour later, fate, perhaps, would have turned in his favor.28 This purely tactical reasoning should be contrasted with
an interpretation that has sometimes been put forward. Taking the defeat to be certain, Napoleon would have found appropriate to his legend to finish it with some grandiose, desperate gesture. This is a wild suggestion, but it is not incompatible with the other, and what both have in common is that they deepen the actor's goals in order to dispel the impression that he acted irrationally.
The decision to cut the army in two suffers from a difficulty of a spatial and material nature that cannot be overcome by reconsidering the ultimate goals. Since the unexpected northward movement of the Prussians made it impossible for Grouchy to carry out both the blocking and pursuit missions, one can attempt to salvage Napoleon's rationality by emphasizing either his misperception of the retreat (Clausewitz's solution) or his prioritizing interposition over pursuit in the orders to Grouchy (Fuller's). As we have seen, the conflicting hypotheses are loosely formulated and have no firm evidence to rely on. A proper model of the Emperor’s choice should help on both scores. Not only will it make each alternative logically more definite, but if it works well, it will discriminate between them, thus acting like a substitute for the missing data.
27 Herbert-Rothe (2005) also compares the two battles of Waterloo and Borodino. 28 This idea comes from Roberts (2005, p. 95).
3. A game-theoretic model of the decision of June 17, 1815
In the following, we model only the actions of Napoleon, Grouchy and Blücher, ignoring Wellington, which can be defended on the ground that he remained fixed at Mont-Saint-Jean after bringing his men there on June 17. In a more debatable simplification, we give Blücher only two possible actions:
B1, march north, then go westward to join Wellington. B2, march north, then go eastward to return to Germany.
We omit a third possibility, B3, which would consist of marching straight east to
Germany. This brings the analysis closer to the actual choice of the Prussians, who did not take B3 into consideration. The omission is more debatable from Napoleon’s point of
view, since he initially expected B3 to occur. However, it would be awkward to formalize
the revision of beliefs that took place on June 17 and 18, and we will assume that, even on Clausewitz's interpretation, Napoleon is at any time uncertain between B1 and B2,
instead of reaching this state of mind only after believing in B3.
No less schematically, two states of the world are possible:
E1, Blücher is badly weakened, E2, Blücher is not badly weakened.
Before knowing which state is realized, Blücher therefore has four strategies at his disposal:
(Bi, Bj) = if E1, then Bi; if E2, then Bj, i, j, = 1, 2.
(By definition, a strategy is a function that associates actions to states of the world recognizable by the player.)
On the French side, another gross simplification will integrate Grouchy into Napoleon, treating them as though the latter were in fact the sole decider. It is somewhat paradoxical that this is less contestable from the marshal’s own view point – his Memoirs describe him as a simple executor of orders – than from the point of view of Napoleon and his staff officers, who overloaded him with complex instructions. Not only does it classically facilitate the game-theoretic analysis to bring the number of players to two, but we will
eschew the difficulty of handling conditional strategies such as the following: chase the Prussian rear-guard if it does not appear that the advance-guard is moving to join the Anglo-Dutch force, drive westward in the opposite case. Yet the minority position à la Fuller would be best formalized by analyzing Grouchy just in terms of such strategies. Thus fused with Grouchy, the player Napoleon has three possible actions:
S1, keep the army together,
S2, detach Grouchy’s forces and send them to block Blücher’s path to Wellington, S3, detach Grouchy’s forces and send them in Blücher’s pursuit.
Now technically reinterpreted, blocking (or interposition) means that the clash between Grouchy and Blücher will occur if Blücher goes west (case S2B1) and not if Blücher goes
east (S2B2), while pursuit means that the clash will occur if Blücher goes the latter way
(case S3B2) and not if he goes the former (S3B1). With these definitions, Grouchy’s
behavior becomes, as intended, mechanical. He rushes where Napoleon commands, and engages in battle or not depending on whether or not he meets Blücher there. Whereas Blücher learns at the interim stage which state of the world is realized, Napoleon does not, and his strategies are therefore constant functions across the states; that is, they are identical to his actions S1, S2, S3.
The following probability parameters represent Napoleon’s beliefs:
k, the probability that Blücher is badly weakened by his defeat at Ligny;
l, the probability of victory for Napoleon’s consolidated army against a united Wellington and Blücher, supposing Blücher was not badly weakened (we will take l to be 0 in a simplified variation);
l′, the probability of victory for Napoleon’s consolidated army against a united
Wellington and Blücher supposing Blücher was badly weakened;
l′′, the probability of victory for Napoleon without Grouchy against a united Wellington and Blücher, supposing Blücher was badly weakened;
m, the probability of victory for Napoleon without Grouchy, and against only Wellington, regardless of the state of Blücher’s forces.
It is automatic to suppose that l′ > l and l′, m > l′′. Other, less obvious inequalities will have to be added to reach a solution.
The model assigns trivial values to all other relevant probability parameters. Thus, it gives a value of 1 to:
the probability of victory for Napoleon’s entire army against Wellington alone, the probability of Grouchy’s victory against Blücher, supposing that Blücher was
badly weakened.
And it gives a value of 0 to:
the probability of victory for Napoleon, without Grouchy, against a united Wellington and Blücher, supposing that Blücher was not badly weakened;
the probability of victory for Grouchy against Blücher, supposing that Blücher was not badly weakened.
It seems inelegant to have so many 0 and 1; however, experimenting with more general assumptions, we have found that they did not appreciably change the conclusions. And the Memorial - although an obviously suspect source - does suggest taking extreme values here. For example, it claims that Grouchy’s detachment was enough to “topple the Prussian rear-guard in whatever position it took” (p. 239). By this token, it is comparatively moderate to assign probability 1 to Grouchy’s victory over Blücher conditional on Blücher being weakened. Still from the Memorial, “if Grouchy had been on field and time had permitted the French army to deploy itself for battle”, one after the other the Emperor would have undone the Anglo-Dutch and Prussian armies (p. 245). Again cautiously, we reserve this probability 1 of victory for the case of Napoleon’s entire army fighting Wellington alone.
The model also includes the following utility values, which reflect Napoleon’s evaluations, just as the probability values reflected his beliefs:
a1, the utility of victory against Wellington,
a2, the utility of victory against Blücher,
b2, the utility of defeat against Blücher,
c, the utility of no confrontation.
Nothing substantial is added if we assume that victories give positive, and defeats negative, utility:
a1 > 0 > b1, a2 > 0 > b2.
However, by a more debatable assumption, we will freely sum the numbers thus defined. In particular,
a1 + a2 = the utility of victory against Wellington and Blücher together b1 + b2 = the utility of defeat against Wellington and Blücher together
In other words, Napoleon’s victory against his two opponents at Mont-Saint-Jean would have the same value as his beating Wellington alone on this field, accompanied by Grouchy’s beating Blücher’s forces elsewhere; and similarly, mutatis mutandis, for the defeats of the French at the hands of both enemies.
We must still evaluate the situation in which Grouchy and Blücher do not meet. This receives the value c = 0 in the case (S3B1) where Blücher marches west and Grouchy
pursues him in vain, and the value θa2 - with θ a parameter between 0 and 1 - in the case
(S2B2) where Blücher marches east and Grouchy engages in a futile block. The second
case differs from the first in that a Prussian retreat without combat represents an additional victory for the French, albeit a much lesser one than would have occurred had Blücher been beaten on the field again.
All that remains in order to represent the situation as a normal or strategic form game is to define Napoleon’s and Blücher’s payoffs for the various outcomes. Using the probabilities k, l, l′, l′′, m and the utilities a1, a2, b1, b2, c, θa2, we calculate Napoleon’s
payoffs by the customary rule of expected utility. Blücher’s payoffs will be supposed to be algebraically opposite to Napoleon’s. In technical terms, this is a zero-sum game, which reflects the nature of this – although not every – military campaign.29 One might
29 Following the previous analysis, at Borodino Napoleon did not aim for Kutuzov’s total annihilation.
however argue that the game is not classically zero-sum. Being also a game of incomplete information, it entails opposite values for expected utilities payoffs, which means that an assumption is made on the probabilities as well as the final payoffs.
We now sketch the resolution, leaving the details for the appendix. The argument will emphasize three expected utility payoffs, denoted V1, V2, V3 in the game matrix:
B1B1 B1B2 B2B1 B2B2
S1 V1
S2 V2
S3 V3
The first step is to associate with each of Napoleon’s strategies the minimum payoff it can bring, taking account of Blücher’s response; this is the strategy’s security payoff. For
S1, the minimizing strategy is B2B1 and the security payment is V1; for S2, they are B2B1
and V2; and for S3, B1B1 and V3. The last two conclusions follow from the automatic
assumptions, but the first needs optional ones on the utility values as well as l, l′, θ. These boil down to an algebraically precise statement that l and l′ are bounded from above.30
The second step compares the strategies S1, S2, S3, supposing that each brings in its
security payoff. The largest of the three numbers - his maxmin - is the greatest amount that Napoleon can guarantee himself, regardless of what Blücher does against him. We will assume that he plays the strategy associated with this value. The comparison between
S1 and S2 depends on the inequality V1 < V2, which is equivalent to a joint restriction on k, l, m and the utility values. This restriction is pleasantly simplified when l = 0.31 The
interaction of the two adversaries. Haywood (1954) also underlines that not every battle is appropriately modeled as a zero-sum game.
30 B
2B1 minimizes the payoff of S1 iff
!
a1+"a2#b1#b2
a1+a2#b1#b2 >l,l'. As θ grows, the central expression
increases towards 1, thus binding l,l' less and less. This is not a very constraining assumption.
31 We deriveV
1 < V2 from m > k(1 – ld) + ld, putting d = (a1 – b1 + a2 – b2) / (a1 – b1). This is a substantial
and constraining assumption, which is simplified as m > k when l = 0. To ensure that the right-hand side is between 0 and 1, we also impose that ld < 1 - another bound on l - and that m > 0, k < 1.
comparison between S3 and S2 depends on the inequality V3 < V2, which follows from a
joint restriction on k, m, θ and some utility values.32 On the basis of these conditions, we conclude that V2 is Napoleon's maxmin and that he plays S2.
The third step is to investigate Blücher’s strategies, B1B1, B1B2, B2B1, B2B2, calculating
security payments for each, and finding the highest of these four numbers, i.e., Blücher’s maxmin, as well as the corresponding strategy. Without further parameter restrictions, these are V2 and B2B1. Making the same behavioral assumption as for Napoleon, we
conclude that Blücher plays B2B1.
The resulting outcome (S2, B2B1) satisfies von Neumann and Morgenstern's solution concept for zero-sum, two-person games. This is not a genuinely interactive concept; rather, as the previous two paragraphs have illustrated, it applies an individual rationality argument twice over, rationality being identified with prudence (each player protects himself against the opponent’s most damaging strategy). However, it is a well known result - holding somewhat more generally than for zero-sum, two-person games - that a solution so defined is also a Cournot-Nash equilibrium, i.e., a pair of mutually optimal responses, and conversely.33 That is to say, S2 is Napoleon’s best response to Blücher’s
choice of B2B1, and B2B1 is Blücher’s best response to Napoleon’s choice of S2. We could
have found the solution (S2, B2B1) just by computing best responses, but this easier
method would have been harder to justify in terms of individual rationality strictly speaking.
The chief tool of zero-sum, two-player games, the minimax theorem, was not directly usable here.34 We obtained the result that Napoleon’s maxmin payoff is equal to the
algebraic opposite of Blücher's maxmin payoff for the initial – so-called pure – strategies of the two players. The theorem would have secured the equality only for the more
32 A sufficient condition for V
3 < V2 is that m > k(1-θ)a2/ (1-k)(a1-b1). The right-hand side is less than 1 if a1-b1 > a2 and either k < ½ or θ> k. The first assumption is fully justified in the historical context of 17
June. Either of last two is conjectural and enters a substantial explanation of the case. There are other sufficient conditions available.
33 See Nash (1950) and Luce and Raiffa (1957, appendix 2).
numerous – so-called mixed – strategies, which amount to randomizing between the pure strategies by means of some probability distribution; hence the need for an ad hoc proof. In limiting case l = 0, some of the parametric conditions vanish, while V1 > V2 becomes
equivalent to m > k, which is easy to interpret: the risk that Blücher is not badly weakened is greater than the risk of losing a duel against Wellington. This assumption is the core of our game-theoretic account of Napoleon’s deliberation on 17 June, which goes informally as follows. First, he discarded S3 because Grouchy could be put to a
better use if he adopted S2. This step is not entirely trivial, because S3 is not dominated by
either S2 or S1.35 Then came the truly difficult choice, that between S1 and S2, which he
resolved in favor of S2 after comparing the two risks just said. Had Napoleon really gone
through these reflections, he would have acted prudently, not as the inveterate gambler of legend. He faced the unpleasant possibility that Blücher, having weathered Ligny better than expected, would defeat Grouchy, but could exclude the worse possibility that Blücher would join forces with Wellington against him alone.
A passage of Memorial (p. 239) suggests the relatively high value for m that we need for the reasoning: the Emperor’s remaining forces were enough to “topple the Anglo-Dutch army” despite a slight numerical disadvantage. Unfortunately, it says nothing to suggest that k was small, except perhaps in the following, roundabout way. Had Napoleon believed the Prussians more diminished than we submit, he would have turned different reproaches on Grouchy. In the already cited passage of p. 245, he describes himself beating Wellington and Blücher one after the other, and he keeps the final victory over the Prussian for himself, leaving it to Grouchy to pin him down for some time, while he was finishing the Englishman. Such a chain of events only makes sense if Blücher was not already annihilated by his defeat at Ligny.36
35 One strategy is dominated by another if it returns a smaller payoff for all the opponents’ responses, in all
states of the world. This game does not give dominated strategies to Napoleon, but it does to Blücher; see the appendix.
36 Inconclusive as they also are, two already discussed staff documents suggest a low k. On June 17,
Bertrand warns Grouchy about Blücher’s remaining possible maneuvers, and Soult’s dispatch of June 18 confirms that Napoleon was concerned about an offensive return of the Prussians.
While distorting Clausewitz’ thesis to an extent, the model brings out the main reason for not accepting it. The thesis maintains that Napoleon dispatched Grouchy for a chase even though the only sensible choice for him was between dispatching Grouchy for interposition and keeping the army together. As can be checked, the conditions for getting the security payoffs associated with S1, S2, S3 are mild or definitional, and
maxmin reasoning excludes S3 from consideration simply on the basis of a definitional
inequality (V3 > V1 follows from l' > l"). So were a Clausewitzian to reject our parametric
restrictions, he would in effect support S1 against S2, but not S3 against these strategies.
Admittedly, Clausewitz implied specific values for some parameters. According to The Campaign, Napoleon believed the Prussians to be badly damaged and was confident to be able to defeat Wellington without Grouchy. This amounts to taking large values for both
k and m. One may add the reinforcing assumption that Napoleon highly valued another full victory against Blücher, i.e., that a2 is large and θ small. This is the Clausewitzian
case parametrically expressed, and it does not affect the overall comparison.
What now for the proNapoleonic position? The model allows his proponents to make some order of their probability assignments. Fuller, for example, could agree with a low value for l, fairly large ones for l' and m, and a weak one for k, and he would likely accept a moderate abatement θ. Enriched with such parametric restrictions, the position offers a logical coherence that the other, given its own preferred restrictions, lacks dramatically. This is not to deny that it involves a difficulty that the other does not. For it leaves unexplained the behavior of Grouchy, who, in our simple dichotomy of chase or block, undertook the former instead of the latter, for which he should have received more or less explicit commands. So the model salvages Napoleon's rationality at the cost of wrecking Grouchy's. But the Clausewitzians makes the opposite trade-off, which involves a worse failure, given what can be inferred from each actor's past performances.
We stressed earlier that the two interpretations could only hypothesize what Napoleon’s commands to Grouchy truly were. Because of this empirical limitation, we used the model in no less than three functions, all of which involve the same set of parametric restrictions. First, the model permitted evaluating the strategies S1, S2, S3; second, it
established that Napoleon, acting rationally, ordered S2 rather than S3; and third, by the
same rationality assumption, it explained this alleged fact as well as the observed fact that he did not order S1. In standard methodological accounts, the explanatory use of
rationality assumptions succeeds a straightforward observational stage. It is said, for example, that preference maximization explains the consumers' demand function for a product, while this function results from market data or questionnaires. But in our study like in many other historical works, what needs explaining is not fully observed. Equivocal reports (the testimonies and dispatches) stand for the missing pieces of information (the oral commands). This is why we used the model also in the function - numbered two above - of clarifying the explanandum. This makes the explanatory process circular, in contradistinction with the consumers' demand case, but not necessarily vicious or inadequate. For there is nothing sinister in a circular reasoning if it makes overall sense of a sufficient amount of sufficiently diverse data (and it is important in this respect that Napoleon's rejection of S1 can be observed). Still, a reasoning of this
style is probably better fitted to assess the comparative value of existing accounts and arguments than to provide a full-fledged explanation of the facts themselves.
4. Response to objections
It is not hard to foresee that the model above will elicit objections similar to those which enlivened the “analytic narrative” controversy. At the most abstract level, game theory itself was called into question. It is well known, for instance, that some games have no solution in any acceptable sense, while others have too many possible solutions, either because there are multiple competing equilibrium concepts, or because the adopted concept - typically the Cournot-Nash equilibrium – allows multiple equilibria to exist.37 Our game-theoretic analysis escapes these difficulties. It uses the Cournot-Nash equilibrium concept in a case – a two-player, zero-sum game – in which specialists have never questioned its appropriateness, because it coincides there with an intuitive concept of individual rationality, namely prudence. Moreover, our particular game has no other pure strategy equilibrium than the one calculated. But it will no doubt be said that our
technical assumptions are ad hoc. Thus the criticism passes naturally from abstract objections to those of the intermediate and lowest plane, which are more challenging because they are more specific. Game-theoretic applications to history risk impoverishing both real events and the theory they draw upon.
We have anticipated on an objection in this group. Grouchy should count among the strategic actors, alongside with Blücher and Napoleon. If this were done, a distinction between strategies and actions would appear on the French side, paralleling that implemented on the Prussian side. Napoleon would have the choice of either remotely controlling Grouchy, or of delegating him the power to act according to what he would find out on the spot. In a game thus refined, the ex post inadequate pursuit might become one of the equilibria instead of being a deviation from the single equilibrium. Although these changes are desirable, the model such as it is will have served at least to illustrate the method and assess the conflicting interpretations.
Another common query in the same group has to do with the actors' objectives, but it does not have much force here. We have already argued for the appropriateness of the zero-sum assumption. The further assumption of additive utility seems defensible on the very same ground, i.e., that nothing short of a crushing victory in the campaign could fulfill the Emperor's objectives. The number and order of the battles mattered little to him as long as he achieved this final result. However, we have not taken the idea to its extreme, since we added only the final, not the expected utilities, which would have altered the conclusions significantly.
There remain the objections of the lowest level of generality, which were the embarrassing ones in the previous controversy. It was said against each selected historical application that it was too ambitious for game theory’s tools. Because our study was aimed specially at avoiding this complaint, a fuller analysis of what is peculiar to military campaigns is now in order; we organize it into six mutually supporting arguments.
First of all, the hierarchical nature of military organization makes it acceptable to concentrate the study on the decisions made by a few key individuals – typically, the general-in-command, his chief-of-staff and the principal lieutenants. In actual fact, the military organization departs from its official definition in a number of ways, and the human material never has the suppleness required to make the leaders’ instructions fully effective. As would any model based on rational choice theories, ours integrates these “frictions” – to use Clausewitz's famous term (On War, I, VII) – by way of probabilizing consequences for the actions of the irreallistically few decision-makers it selects. The limit of this method is that it rules out some possibly relevant interactions. Thus, to treat the discipline among rank-and-file as a stochastic phenomenon is to forget that it depends on a range of activity on the leaders’ part – demonstrations of courage, promises, threats and exhortations – which do not normally enter the model’s list of actions. To this, we may reply that the neglected interaction is not always significant to the same degree, and that the empirical material itself should serve as a touchstone. When an army disbands, the modeler must bring forth the relation between the leaders and the troops; when it obeys orders, as it did on June 18 before the tragic denouement, he may pass over it. In the second place, as a campaign proceeds – and even more clearly once a battle is engaged – each of the general-in-command’s decisions is easy to locate in time and space, and so are, in principle, the staff members’ and lieutenants’ induced decisions.38 The proximate effects of all these changes are movements of such and such part of the army at a certain hour and in a certain direction, which are, again in principle, ascertainable. The military distinction between a strategy and a tactic becomes relevant at this juncture. The former organizes the movements of a campaign, which prepare for battle or link multiple battles in view of the final victory, while the latter arranges the movements of a given battle in order to win it out.39 This is a means-ends hierarchy, but it also taken to express differences in spatio-temporal locations - the movements of a campaign being more remote than those of a battle - and to reflect the hierarchical
38 We add “in principle” because the uncertainty grows as the level of command decreases. For instance,
there is no completely firm evidence of who exactly ordered the main cavalry charge on June 18, and some historians have questioned the received view that Ney did.
organization - the general-in-command being the sole responsible for the strategy, whereas he shares or delegates responsibilities on the tactic.40 The June 1815 sequence of events illustrates this multiple distinction neatly. On the basis of his plan of campaign, Napoleon entrusted Ney and Grouchy with the supervision of battles that were likely to be pitched in remote directions. Even on the battlefield of Waterloo, where he was present, he left much to Ney to decide. For the purpose of an “analytic narrative”, it is very convenient to be able to investigate strategic decisions independently of tactical ones, especially if this division coincides with one in terms of individual actors.
Third, the overall goal is determined from without and once and for all; it is to win out the battle or the campaign, as the case may be. According to the older military definitions, the first occurs with the final occupation of the field, and the second with the conquest of a province or stronghold. The modern concept of a victorious campaign or battle is more abstract, holding it to be the destruction of the opposing forces or, failing that, their significant weakening, with their own admission of the fact if possible. This much is suggested by On War, although there has been some debate on Clausewitz's precise meaning.41 The plural understanding of victory gives birth to some ambiguity in the assessment of success or failure as one goes back in time.42 But this is by and large a second-order problem, which should be set against the broadly correct point that, in the present context, the teleological component of reasons is both fixed and simple.
Fourth, even a campaign decision of the highest degree of complexity is in principle assessed in terms of its final consequences on the field. An idealized general-in-command would reduce the content of his decisions to that of their successive effects, then pass back step by step from the evaluations of the latter to the comparative evaluation of the former. Seen from this consequentialist perspective, the choice of June 17 was relevant
40 Before Clausewitz, Bülow emphasized the spatio-temporal and organizational aspects, i.e., the tactic has
to do with military movements within the angle of vision or the possible reach of the general-in-command, and the strategy with what goes beyond.
41 Arguing from the relationship of politics to military activity in On War (VIII), Aron (1976) concludes
that Clausewitz promoted a novel conception of victory. But Paret (1992, p. 106) makes it clear that he did not altogether give up the notion that the military objective is to conquer terrain.
42 Even some Napoleonic events are not easy to classify. With Borodino, Eylau is the classic example of a
